Answers to two questions posed by Farhi concerning additive bases

Abstract

Let A be an asymptotic basis for N and X a finite subset of A such that A\X is still an asymptotic basis. Farhi recently proved a new batch of upper bounds for the order of A\X in terms of the order of A and a variety of parameters related to the set X. He posed two questions concerning possible improvements to his bounds. In this note, we answer both questions.

7 pages, no figures. This is v3 : I found a gap in the proof of Lemma 3.2 of v2. This has now been corrected and the same result is Lemma 3.3 in this version